The question does not specify the expected number of flexing cycles across the device lifetime. For applications where the FPC will be flexed just once at installation, such as connections between the LCD panel and attached backpack controller board, pretty much anything goes. At worst, infantile death of the FPC if it happens, will be detected in a test run.
Assuming multiple flexing cycles:
The location of the via inherently becomes a weak point. Given that flexing already creates stress on the copper layers, this is a conduction breakage waiting to happen. You will notice that if there ever are vias on FPC, they are found on the parts unlikely to bend.
The copper used must also be the thinnest possible, to minimize risk of fracture. This means 1 ounce copper, or thinner even, if the application can stand it.
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